<h2>Range of a Quadratic Function</h2>
The range tells us the possible <em>y</em>-values that occur in the function.
When describing the range, we can write an inequality using <em>y</em>.
When describing the range of a quadratic function, we typically use the ≥ or ≤ symbols when writing the inequality.
To write the range of a quadratic function,
- Find the vertex
- Determine whether the parabola opens up or down
- Set <em>y</em> ≥ or ≤ the y-coordinate of the vertex
<h2>Solving the Question</h2>
We're given:
- Vertex at (0,4)
- Other points on the graph: (-2,0), (-1,3), (1,3), (2,0)
Because we're directly given the vertex, we just have to determine now whether the parabola opens up or down.
- If the other points on the graph always have a lower <em>y-</em>coordinate value, then the graph opens down
- If the other points on the graph always have a greater <em>y-</em>coordinate value, then the graph opens up
The other points that fall on the graph that we're given all have a lower y-coordinate value than 4, that means this parabola opens down.
Therefore, all other y-values for the function will be less than 4.
Therefore, y ≤ 4.
<h2>Answer</h2>
y ≤ 4
